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Asymptotically exact inference in conditional moment inequality models

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  • Armstrong, Timothy B.

Abstract

This paper derives the rate of convergence and asymptotic distribution for a class of Kolmogorov–Smirnov style test statistics for conditional moment inequality models for parameters on the boundary of the identified set under general conditions. Using these results, I propose tests that are more powerful than existing approaches for choosing critical values for this test statistic. I quantify the power improvement by showing that the new tests can detect alternatives that converge to points on the identified set at a faster rate than those detected by existing approaches. A Monte Carlo study confirms that the tests and the asymptotic approximations they use perform well in finite samples. In an application to a regression of prescription drug expenditures on income with interval data from the Health and Retirement Study, confidence regions based on the new tests are substantially tighter than those based on existing methods.

Suggested Citation

  • Armstrong, Timothy B., 2015. "Asymptotically exact inference in conditional moment inequality models," Journal of Econometrics, Elsevier, vol. 186(1), pages 51-65.
  • Handle: RePEc:eee:econom:v:186:y:2015:i:1:p:51-65
    DOI: 10.1016/j.jeconom.2015.01.002
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    Cited by:

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    3. Andrew Chesher & Adam Rosen, 2018. "Generalized instrumental variable models, methods, and applications," CeMMAP working papers CWP43/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Aradillas-López, Andrés & Gandhi, Amit & Quint, Daniel, 2016. "A simple test for moment inequality models with an application to English auctions," Journal of Econometrics, Elsevier, vol. 194(1), pages 96-115.
    5. Andrews, Donald W.K. & Shi, Xiaoxia, 2017. "Inference based on many conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 196(2), pages 275-287.
    6. Christian Bontemps & Thierry Magnac, 2017. "Set Identification, Moment Restrictions, and Inference," Annual Review of Economics, Annual Reviews, vol. 9(1), pages 103-129, September.
    7. Armstrong, Timothy B., 2018. "On the choice of test statistic for conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 203(2), pages 241-255.
    8. Nicky L. Grant & Richard J. Smith, 2018. "GEL-based inference with unconditional moment inequality restrictions," CeMMAP working papers CWP23/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Christoph Breunig, 2015. "Testing Missing at Random using Instrumental Variables," SFB 649 Discussion Papers SFB649DP2015-016, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    10. Nicky L. Grant & Richard J. Smith, 2018. "GEL-Based Inference from Unconditional Moment Inequality Restrictions," Economics Discussion Paper Series 1802, Economics, The University of Manchester.

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